The gap is for two reasons, the first operational, the second infrastructure related.
Operationally, GN need time to completely separate out the crew working arrangements, as well as stabling and staffing of stations. That will take at least two timetable changes to bed in, from the point that an official decision to split is made.
Secondly, TfL also need time after the decision is made for their teams to understand what they have to work with, and work out what they want to do with it. Rebranding, rejigging the ticketing, looking at increasing frequency, and tendering operation of the line will also take about a year after the decision is made.
Collectively, this means that even though a decision to transfer to TfL is expected at the end of 2026, it will still take time after that point for TfL to have all their ducks in a row for it to become an Overground line.
In terms of benefit, the biggest is psychological, the act of branding it as an Overground service will be a big change. It's likely that service frequencies will improve, but that's speculative at the moment. Apart from that, the best comparison is probably the South London line, where the change to Overground came with a massive increase in ridership, simply by putting it on the tube map.